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• Math
Recall binomial series follows: `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4+...` To...

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• Math
Recall a binomial series follows: `(1+x)^k=sum_(n=0)^oo _(k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4+` ... To...

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1 educator answer.

• Math
Binomial series is an example of an infinite series. When it is convergent at `|x|lt1` , we may follow the sum of the binomial series as `(1+x)^k` where `k` is any number. The formula will be:...

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• Math
Recall binomial series that is convergent when `|x|lt1` follows: `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3...

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• Math
Binomial series is an example of an infinite series. When it is convergent at `|x|lt1` , we may follow the sum of the binomial series as `(1+x)^k` where `k` is any number. We may follow the...

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• Math
Recall binomial series that is convergent when `|x|lt1` follows: `(1+x)^k=sum_(n=0)^oo _(k(k-1)(k-2)...(k-n+1))/(n!)` or`(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3...

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• Math
Recall binomial series that is convergent when `|x|lt1` follows: `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n` or `(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x) ` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at` x=c` . The general formula for...

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1 educator answer.

• Math
aylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of ` f^n(x)` centered at ` x=c` . The general formula for...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of` f^n(x)` centered at `x=c` . The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of `f^n(x)` centered at` x=a` . The general formula for...

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• Math
A power series centered at `c=0` is follows the formula: `sum_(n=0)^oo a_nx^n = a_0+a_1x+a_2x^2+a_3x^3+...` The given function `f(x)= 3/(3x+4)` resembles the power series: `(1+x)^k = sum_(n=0)^oo...

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• Math
Recall the Root test determines the limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or `lim_(n-gtoo) |(a_n)|^(1/n)= L` Then, we follow the conditions: a) `Llt1` then the series is absolutely...

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• Math
Recall the Root test determines the limit as: `lim_(n-gtoo) |(a_n)^(1/n)|= L` Then, we follow the conditions: a) `Llt1` then the series is absolutely convergent b)` Lgt1` then the series is...

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• Math
`sum_(n=0)^oo (2n)! x^(2n)/(n!)` To find radius of convergence of a series `sum` `a_n` , apply the Ratio Test. `L = lim_(n->oo) |a_(n+1)/a_n|` `L=lim_(n->oo)| ((2(n+1))!...

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• Math
`sum_(n=0)^oo x^(2n)/((2n)!)` To find the radius of convergence of a series `sum` `a_n` , apply the Ratio Test. `L = lim_(n->oo) |a_(n+1)/a_n|` `L=lim_(n->oo) |...

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• Math
`sum_(n=0)^oo (-1)^n x^n/5^n` To determine the radius of convergence of a series `sum` `a_n` , apply the Root Test. `L = lim_(n->oo) root(n)(|a_n|)` `L=lim_(n->oo) root(n)(|(-1)^nx^n/5^n|)`...

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• Math
`sum_(n=1)^oo (4x)^n/n^2` To find radius of convergence of a series `sum` `a_n` , apply the Ratio Test. `L = lim_(n->oo) |a_(n+1)/a_n|` `L=lim_(n->oo) | (4x)^(n+1)/(n+1)^2 * n^2/(4x)^n|`...

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• Math
`sum_(n=0)^ oo (3x)^n` To find the radius of convergence of a series `sum` `a_n` , apply the Root Test. `L=lim_(n->oo) root(n)(|a_n|)` `L=lim_(n->oo) root(n)(|(3x)^n|)` `L= lim_(n->oo)...

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• Math
`sum_(n=0)^oo (-1)^n(x^n)/(n+1)` To find the radius of convergence of a series `sum` `a_n` , apply the Ratio Test. `L = lim_(n->oo) |a_(n+1)/a_n|` `L=lim_(n->oo) |((-1)^(n+1)...

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1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of` f^n(x)` centered at `x=c` . The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x) ` centered at `x=c` . The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c ` .The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c.` The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of` f^n(x)` centered at `x=c.` The general formula for...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

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• Math
Maclaurin series is a special case of Taylor series that is centered at `a=0` . The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

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1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at `a=0` . The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

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1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at `x=0` . The expansion of the function `f(x)` about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

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1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at `c=0` . The expansion of the function about `0` follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at `c=0` . The expansion of the function about `0` follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at `c=0` . The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about `0` follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at `a=0` . The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n` or `f(x)=...

Asked by enotes on via web

1 educator answer.

• Math
`sum_(n=0)^oo3(x-4)^n` Given series is a geometric series with ratio `r=(x-4)` , so the series converges if `|r|<1` `|x-4|<1` `=>-1<(x-4)<1` `=>3<x<5` Given series...

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• Math
`sum_(n=0)^oo((x-3)/5)^n` It is a geometric series with common ratio (r)`=(x-3)/5` , so the series converges if `|r|<1` `|(x-3)/5|<1` `=>-1<(x-3)/5<1` `=>-5<(x-3)<5`...

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• Math
`sum_(n=0)^oo2(x/3)^n` Given series is a geometric series with ratio `r=x/3` , so the series converges if `|r|<1` `|x/3|<1` `=>-1<x/3<1` `=>-3<x<3` So the given series...

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• Math
To determine the convergence or divergence of a series `sum a_n` using Root test, we evaluate a limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or `lim_(n-gtoo) |a_n|^(1/n)= L` Then, we follow the...

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• Math
To determine the convergence or divergence of a series `sum a_n` using Root test, we evaluate a limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or `lim_(n-gtoo) |a_n|^(1/n)= L` Then, we follow the...

Asked by enotes on via web

1 educator answer.

• Math
To apply Root test on a series `sum a_n` , we determine the limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or `lim_(n-gtoo) |a_n|^(1/n)= L` Then, we follow the conditions: a)...

Asked by enotes on via web

1 educator answer.

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